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CHAPTER 2

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2.0 INSTRUMENTATION DETAILS

The instrumentation systems are described in detail in this chapter.

The systems description, brief specifications along with measurements are

discussed instrumentation wise. The instrumentation systems are precision

C-Band radars17, wind profiler and transponder on board the SARAL

satellite. The instruments are calibrated and the random noise in the

measurements is removed before using the data for different applications.

The applications include applying digital filter on radar measurements to

obtain state vector estimation for launch vehicle. Brief description of the

launch vehicles for which state estimation was carried out is also included.

At the end, the description of Advanced Technology Vehicle is also provided

for which, the sustainer ignition is initiated from ground, based on radar

data. Measurements from wind profiler and the processing techniques used

are very important in view of the results being used for wind biasing on the

day of launch. The details of wind profiler are also provided in this section.

2.1 C-BAND TRACKING RADAR

The subsystems in a C-band tracking radar are as follows

Transmitter

Digital Receiver System (DRS)

Range Tracking System (RTS)

Angle Tracking System (ATS) & antenna electronics

Data Processing System (DPS)

Control Console and Display System (CCDS)

Local Oscillator (LO) and Automatic Frequency Control (AFC)

Power distribution unit

RF Head and Simulator (RFHS)

Target simulator

Boresight Tower (BST)

The transmitter is designed to generate pulsed peak power of 1MW at

the selected PRF and the pulse width satisfying the duty ratio limitation of

the transmitting tube. It is useful for long range skin tracking of hard

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targets or for interrogating the launch vehicle borne transponders for very

long range tracking.

The digital receiver sub-system employs high speed ADCs and digital

signal processing techniques instead of the conventional analog IF receiver.

It receives the three IF signals from RF head, namely, sum (Σ), and

differences ∆Az and ∆El. It is designed to provide a dynamic range of 80 dB.

It computes the range error for RTS and the angle errors (Azimuth and

Elevation) for the ATS. The DRS and its interfaces are shown in Figure 2.1.

RTS

DIGRX

VMESBC

DPSSETHERNET LINK

CLOCK

VME BUS

SAMPLING

GATE

RF MODULE

∆ AZ CH ( 30 MHz IF )∆ EL CH ( 30 MHz IF )Σ CH ( 30 MHz IF )

ATS

AZIMUTH ANGLE ERROR

ELEVATION ANGLE ERROR

ENVELOPEDETECTOR

LOAS

RTS, CCDS

& LOAS

RFHS

ETHERNET LINK

ETHERNET LINK

Figure – 2.1 DRS and its interfaces with other subsystems

The Range Tracking Subsystem (RTS) acquires and tracks the return

signals from the target and provides accurate range data. Range tracking is

the process of continuously measuring the delay between the transmitted

pulse and the target return. The range of the target, R is determined by R =

(C x T) /2, where ‘C’ is Velocity of the light and ‘T’ is the time delay between

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the transmitted pulse and target return. It provides continuous and

unambiguous range data even during blind zones.

RTS operates in different operating modes like manual, designate and

auto tracking as per the selection of the user. In the manual mode, the user

can move the range using the joystick control provided on the control

console. In the case of designate mode, range is updated as per the

designated data received from the DPS. In Auto tracking mode, RTS receives

the tracking error from the DRS, predicts the target range using α-β tracking

algorithm and adjusts the tracking gate delay as per the predicted range.

RTS incorporates the range tracking features like Auto acquisition, zone

verification, Phase IN & Phase OUT, Track transfer and mixed mode

tracking.

In auto-track mode the range error received from digital receiver using

split gate technique, is fed to α, β, γ filter18 with appropriate filter coefficients

as per the bandwidth required (BW-1, BW-2 or BW-3). In adaptive

bandwidth control, the bandwidth is increased / decreased by comparing

the average lag error and thermal noise computed. Range error modified by

α, β, γ filter is immediately used to update the range data (magnitude and

polarity).

In addition to the tracking functionalities, RTS generates the timing

signals and implements control logic required for different subsystems in the

RADAR. Some of these include zero km reference; Tracking pointer

reference; Local Ocillator selection logic for mixed mode operation; Pulse

code generation logic for the transmitter. RTS also has the PRF

synchronization19 circuitry for the synchronization of the radar with other

radars in the network.

The Angle Tracking System (ATS) positions the antenna precisely in

azimuth and elevation axes as per the given reference angle in different

modes of operation. The elevation and azimuth axes are driven using two

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brushless DC servomotors per axis in counter-torque mode. The motor

shafts are coupled to individual gearboxes that are mechanically

synchronized through a slewing ring bearing assembly. The ATS and its

interfaces are shown in Figure 2.2.

The major function of Angle Tracking Subsystem is to precisely steer

the antenna within the beam width during auto tracking using the RF error

received from DRS. During auto tracking the servo system receives angle

error data from DRS. The digital receiver operates on the principle of

Amplitude Comparison Monopulse Tracking technique where four antenna

elements illuminate the target at the same time.

Based on the target position w.r.t. the antenna axis, differential

amplitudes are generated along with the direction in both axes, e.g. azimuth

and elevation. These amplitude differences are then converted to angular

error in ‘mil’ using S-curve20 calibration method, which is used for auto

tracking by servo system.

Monopulse tracking21 requires three receiver channels to track a

target. The three channels are named as Sum, Azimuth Difference and

Elevation Difference. Sum beam has peak gain and the difference beam has

a deep null at boresight axis. The sum channel along with the difference

channels is used to generate error signals to drive the servo system to

minimise the error in the respective axis.

Apart from auto tracking, the servo system receives directly the

reference angle data in both axes from different sources like mission

computers, program track (predicted trajectory), space point designate, open

sight encoders etc. The ATS generates the reference angles in manual mode

by making use of the position of joysticks of azimuth and elevation axes. It

can also track targets in TV track mode or IR track mode with associated

sensors22 and tracker card.

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Figure – 2.2 Interface block diagram of ATS with other subsystems

The Data Processing Subsystem (DPS) is the centralized data

acquisition subsystem and communicates with other subsystems of the

radar and also with other elements of SHAR range, like mission

computers and MCC. DPS is a PowerPC processor based system with Real

time Operating System. It also has a Linux based single board computer

(SBC) for the Graphical User Interface (GUI). The communication with

other subsystems of the radar is either through Ethernet or serial

interface (Boresight, Polariser interfaces) for data transfer.

An

gle

Tra

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g S

ub

syst

em (

AT

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Azi

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Cab

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(D

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)

AT

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Ant

enna

Con

trol

& S

tatu

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Dat

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CLK

Sup

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&

sign

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Supply & signals

Con

figur

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d de

sign

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data

from

DP

S,

Ang

le e

rror

s fr

om D

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, Com

man

d da

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Joys

tick

data

, TV

/IR e

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from

AT

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BO

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Open sight Encoders Data

EL

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oder

s da

ta &

CLK

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DPS exchanges commands, status and data with other subsystems

of the radar, as well with other radars and mission computers. It stores

the acquired data and status of the subsystems along with on-axis

designate data, launch countdown time and universal time. It performs

many real-time and off-line functions including all types of calibrations.

The interface detail of the DPS subsystems with various subsystems in

the radar and mission computers is shown in Figure 2.3. It receives the

antenna pointing information from the mission computers in real time to

position the antenna in case of loss of tracking.

Figure – 2.3 Interface of DPS with other subsystems

The Control Console and Radar Display Subsystem is real-time front

end of the radar for the user. It displays the target echo in the form of A-

scope, F-scope and PPI. It also displays the real-time tracking parameters

and the sub-system health status. It provides real-time controls of different

tracking modes and other auxiliary controls using hard and soft switches.

The antenna subsystem consists of the Radiating elements, Polarizer

assembly, Monopulse comparator assembly, Crossguide Dual Direction

coupler (for Sum channel), Circulator (for Sum channel) Waveguide

VME Power Supply Card

PowerPC SBC

x86 SBC

KB

&

Mou

se

VGA Monitor

CD RW

Printer

VME 64X

Ethernet Switch

External Switch

DI Card

DI Card

CD

T R

eade

r

UT

Rea

der

To Polarizer

To Boresight

To radar subsystems

To MC & MCC

VME Power Supply Card

VME Power Supply Card

PowerPC SBC

PowerPC SBC

x86 SBCx86 SBC

KB

&

Mou

se

VGA Monitor

CD RW

Printer

VME 64X

Ethernet Switch

External Switch

Ethernet Switch

External Switch

DI Card

DI Card

DI Card

DI Card

CD

T R

eade

r

UT

Rea

der

To Polarizer

To Boresight

To radar subsystems

To MC & MCC

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assembly and TR Limiter. Figure 2.4 shows the block diagram of the

antenna subsystem.

Figure - 2.4 Block diagram of the Antenna Subsystem

One of the major requirements for the radar antenna is the capability

to operate in different polarizations viz. Linear Vertical, Linear Horizontal,

Right circular and Left circular. By controlling the electric field direction

with respect to the propagation axis, it is possible to meet all the

polarisation requirements. Direction control of the electric field calls for the

rotation of some of the feed components and the same is accomplished in

polariser assembly. The use of rotating joints in polariser assembly will

enable the rotation of the electrical field direction, which in turn gives the

flexibility of achieving required polarization. The feed configuration is shown

in Figure 2.5. For different relative positions of the two polariser sections in

polariser assembly, one of the four polarisations can be achieved.

The Boresight (BST) subsystem for the tracking radar is designed to

have all the facilities to check the performance and features of various

subsystems of the radar and also to calibrate the radar. This system is

designed to test and calibrate the complete radar including antenna and

feed with complete control from radar. BST facilitates simulation of a

target at required frequency, polarization and S/N along with dynamics in

range. It facilitates all the four different polarization types. It is used to

verify the antenna pattern in azimuth and elevation at different

frequencies and polarizations. It provides facility for automatic phase

matching verification of 3 channels of monopulse receiver23, with the help

of CW/Pulse mode of the RF source. Moving target simulation is done at

required velocity and frequency. It also provides the facility for S-curve

Pol

ariz

er

Rad

iatin

g E

le.

Mon

opul

se

Com

p.

DDC Circulator

TRL (∆Az)

TRL (Sum)

TRL (∆El)

RF

HS

To TxPol

ariz

er

Rad

iatin

g E

le.

Mon

opul

se

Com

p.

DDC Circulator

TRL (∆Az)

TRL (Sum)

TRL (∆El)

RF

HS

To Tx

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calibration of the radar at the required frequency, polarization and S/N

levels. It is useful for evaluating the step response and bandwidth

measurement of angle servo subsystem of the radar in azimuth and

elevation axes.

Figure – 2.5 Feed Assembly

Even though utmost care is taken during the installation of a radar,

minor installation offsets, mount and antenna misalignment and the delays

in the circuitry will manifest errors in the measurements. Hence, radar

calibration24,25 and usage of root mean square are essential. These are dealt

with in detail in subsequent chapters.

2.2 TYPES OF LAUNCH VEHICLES

India launched its first rocket from the Thumba Equatorial Launching

Station in 1963. Gradually, the horizons of the Indian space programme

expanded. During the 60s, many sounding rockets were launched. In the

early 70s, ISRO initiated plans to develop and design indigenous satellites

and their launch vehicles along with development of sounding rockets. On

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October 9, 1971, the first rocket was launched from Sriharikota. It was the

RH-125 sounding rocket.

On July 18, 1980 India joined the exclusive group of nations

possessing their own launch capability when ISRO’s first generation satellite

launch vehicle SLV-3 took off from Sriharikota Range and successfully put

the Rohini satellite into a near earth orbit. Subsequently, an augmented

version of SLV-3, called the Augmented Satellite Launch Vehicle (ASLV), was

successfully launched on May 20, 1992 placing the SROSS-C26 satellite into

a low earth orbit. These vehicles had all stages with solid propellant.

During 80s, ISRO started designing and developing the PSLV which

has become the workhorse vehicle for ISRO. The PSLV has both stages with

solid and liquid propellants. This vehicle was initially intended for launching

remote sensing satellites in SSPO. However, its versatility was proved when

it could place spacecrafts in GTO and also used for Chandrayaan-I, Mars

Orbiter Mission and re-entry missions.

However, due to constraints of liquid engines to lift heavier payloads,

a new launch vehicle, the GSLV, with cryogenic upper stage was designed

for placing two ton class of spacecrafts in GTO. Now, ISRO is developing the

GSLV-MkIII which can carry four ton class of spacecrafts to GTO.

A variety of data processing techniques were designed and developed

to cater to the various requirements of all these missions depending on their

trajectories.

POLAR SATELLITE LAUNCH VEHICLE - PSLV

Polar Satellite Launch Vehicle is a medium lift launcher that can

reach a variety of orbits including LEO, SSPO and GTO. PSLV is a four-stage

rocket that uses a combination of liquid fuelled and solid fuelled rocket

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stages. The vehicle can fly in three different configurations to adjust for

mission requirements.

The standard version of PSLV features six strap-on solid rocket

boosters clustered around its first stage which itself is also solid fuelled. The

second stage is liquid fuelled while the third stage is a solid rocket

motor. The upper stage of the PSLV uses liquid propellant. The launcher

stands 44.4 meters tall and has a diameter of 2.8 meters. Depending on the

launcher's configuration, PSLV weighs 229 tons, 296 tons or 320 tons at lift

off. In addition to the first or standard PSLV version, it can fly in its Core

Alone (CA) configuration, without the six solid rocket boosters and less

propellant in the tanks of its upper stage. This configuration is used for

missions that feature small payloads. PSLV has an XL (Extra Length) version

that launches with additional propellant in its solid rocket boosters to

increase payload capability27.

The first stage of the PSLV, is a solid fuelled rocket stage. It is 20.34

meters long and 2.8 meters in diameter with an empty mass of 30 tons. The

stage contains 138 tons of solid propellant at liftoff.

The second stage of the PSLV rocket is 2.8 meters in diameter, 12.8

meters long and has a liftoff mass of 46 tons with an empty mass of 5 tons.

The stage uses liquid fuel and liquid oxidizer for developing thrust. It is

powered by a single 799-KN Vikas engine.

The third stage is a solid rocket motor and has a reduced diameter of

2.02 meter and a length of 3.54 meters. It has an empty mass of around 1

ton and a liftoff weight of around 7 tons.

The upper stage of the PSLV launcher uses liquid fuel and liquid

oxidizer for developing thrust. The stage is 2.02 meters in diameter and has

a length of 2.60 meters with an empty mass of 0.9 tons. It contains around

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2.5 tons of propellant when flying on the standard version and XL

configuration and 1.6 tons when flying atop the CA configuration.

PSLV Payload Fairing is 3.2 meters in diameter, 8.3 meters long and

weighs around 1.1 tons. It consists of two all-aluminum halves that consist

of different sections. The vehicle injects the satellite into intended orbit

around 1800s after liftoff.

The various versions of PSLV are shown in Figure 2.6. PSLV can carry

a payload of 3.2T to a LEO, 1.4T to a GTO and 1.1T to 1.8T to SSO

depending on the configuration.

First Version Core Alone XL Strapon

Figure – 2.6 Various variants of PSLV

GEO SYNCHRONOUS SATELLITE LAUNCH VEHICLE - GSLV

Geosynchronous Satellite Launch Vehicle is three-stage vehicle with

four liquid fuelled strap-ons engines. GSLV28 uses a combination of solid

fuelled, liquid-fuelled and cryogenic fuelled stages. The vehicle weighs 414

tons at liftoff and stands 49 meters tall. Figure 2.7 shows the GSLV on a

launch pad ready to lift off.

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Figure – 2.7 GSLV at umbilical tower in SLP launch complex.

The core stage of the GSLV is a solid fuelled rocket stage and is

derived from the core stage of the PSLV. It has an inert mass of 28 tons and

holds 138 tons solid propellant. The stage is 20.1 meters long and 2.8

meters in diameter.

Four liquid-fuelled strap-ons are clustered around the core stage of

the vehicle. Each is 2.1 meters in diameter and 19.7 meters long. Each

strap-on has two Aluminum propellant tanks that can hold about 40 tons of

liquid fuel and liquid oxidizer.

The second stage of the GSLV also uses liquid fuel and liquid oxidizer.

It has a launch mass of 40 tons and is 11.6 meters long and 2.8 meters in

diameter. The third stage of the GSLV MKII is an Indian-built cryogenic

upper stage. It is 8.7 meters long and 2.8 meters in diameter. The inert

mass of the third stage is about 2 tons.

The fairing of the GSLV is 3.4 meters in diameter and 7.8 meters in

length offering enough space for a variety of payloads. The vehicle injects the

satellite into intended orbit around 1600s after liftoff.

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LAUNCH VEHICLE MARK III (LVM3)

The Launch Vehicle Mark III is currently under development. GSLV

Mk III is conceived and designed to make ISRO fully self reliant in launching

heavier communication satellites of INSAT-4 class, which weigh 4.5 tons to

5 tons. The vehicle envisages multi-mission launch capability for GTO, LEO,

Polar and intermediate circular orbits. Figure 2.8 shows the GSLV-MKIII28

vehicle at the SLP.

Figure – 2.8 GSLV-MkIII at umbilical tower in SLP launch complex.

LVM3 is designed to be a three stage vehicle. It stands 42.4 meters tall

with a lift off weight of 630 tons. The first stage comprises of two identical

large solid boosters with 200 tons of solid propellant, which is strapped on

to the second stage, the L-110 liquid stage. The third stage is the C-25

cryogenic stage. The payload fairing is also larger measuring 5 meters in

diameter and can accommodate a payload volume of 100 cu m. Realization

of GSLV Mk-III will help ISRO to put heavier satellites into orbit. Each

booster is 3.2 meters in diameter and is 25 meters long. The core stage,

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designated as L-110, is a 4-meter diameter liquid-fuelled stage containing

110 tons of propellant.

The cryogenic upper stage is designated as C-25 and will be powered

by the Indian-developed CE-20 engine burning cryogenic propellants. It is 4

meter in diameter and 8.2 meter long. It contains 25 tons of propellant.

ADVANCE TECHNOLOGY VEHICLE (ATV)

Advanced Technology Vehicle (ATV) is ISRO’s new generation high

performance sounding rocket, offering a cost effective test bed for

demonstrating Air-Breathing Propulsion (ABP) technology. This is the largest

and heaviest sounding rocket that ISRO has developed till date. ATV D-

series vehicles are configured as a two stage, unguided, spinning fin

stabilized vehicles with two protruding passive scramjet engines.

The ATV-D01, weighing 3 tons at lift-off, carried a passive scramjet

engine combustor module as a test bed for the demonstration of Air-

Breathing Propulsion29 Technology. During the flight, vehicle successfully

dwelled for 7 seconds in the desired conditions of Mach number (6+0.5) and

dynamic pressure (80+35 kPa). These conditions are required for a stable

ignition of active scramjet engine combustor module. Figure 2.9 shows the

ATV-D01 assembled on the launcher at the sounding rocket complex.

Figure – 2.9 ATV-D01 at sounding rocket launch complex.

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The first flight of ATV-D01 was designated towards vehicle

characterization. The vehicle carries passive scramjet engines to the Mach

number-dynamic pressure (M-q) window in which active Air-Breathing

Technology has to be demonstrated. The first stage called the booster and

the second stage called the sustainer are identical RH 560M motors having

solid propellant. The nosecone houses Telemetry, Tracking, Command, Real

Time Decision (RTD), sequencing and instrumentation payloads.

The two passive scramjet engines are fitted at the rear end of the

sustainer between the non-cruciform fins and on the fin shroud. Fuel feed

system carries the fuel storage and feed system for scramjet engines. To

achieve the required M-q window and maximum dwell time, a novel flight

profile is designed with two Real Time Decisions (RTDs) for accommodating

the stage performance deviations, if any and command was issued from

ground.

Advanced Technology Vehicle has the unique capability to take a

payload of 0.2-0.4 tons up to an altitude of 800 km. Ascent of the vehicle in

a direct vertical profile makes it an excellent platform for space research,

best suited for the studies of upper atmospheric features and short period

transient phenomena/events in the atmosphere. ATV also provides a new

rocket user discipline for the study of microgravity30 conditions.

It can provide up to 10 minutes of microgravity at levels better than

100µg which can be used for microgravity experiments in fluid physics,

combustion research, materials sciences, and biology as well as to perform

precursor experiments for launch vehicles, satellites and manned missions.

Micro and Nano satellites have become increasingly popular these days.

Launch availability for such small satellites are heavily dependent on piggy-

back ride on launch vehicles. The ATV as a cost-effective small launch

vehicle has got tremendous potential for suborbital flights.

2.3 WIND PROFILER RADAR

Wind profilers are pulsed radar systems which provide continuous

atmospheric winds data on a continuous basis with very good temporal and

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spatial resolutions. The advantages of the wind profilers are that they

provide a very good temporal and spatial resolution data on a continuous

basis, giving precise information in real time / near real time and can detect

wind shears.

For ISRO’s launch vehicle trajectory design, the day of launch wind

biasing31 is being done to have minimal angle of attack (α) throughout its

atmospheric flight. The vehicle is steered so that minimum Qα is achieved,

where Q is the dynamic pressure. This requires precise data about the wind

and as near as possible to the launch time. To acquire such data, wind

profiler RADAR is an ideal instrument.

Due to turbulence in the atmosphere, the refractive index variations

corresponding to scale sizes of half the wavelength of the transmitting

frequency will backscatter return signals towards the radar.

The horizontal wind is measured by oblique beams in orthogonal

directions (e.g. east and north). The beams are tilted up to 20 degrees from

the zenith, and the doppler shift of the echoes in each direction are

estimated to determine the wind speed and direction. The main principle of

the operation is shown in Figure 2.10.

Figure – 2.10 Principle of Operation.

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It uses a fully active aperture array of solid state Transmit-Receive

(TR) modules. It operates in three modes – Spaced Antenna (SA), Doppler

Beam Steering (DBS1) and DBS2 – based on the height.

Power aperture product is the figure of merit. Higher the power

aperture product, better is the sensitivity of the system. The typical single

pulse SNRs are as low as –50 dB in the case of atmospheric returns for weak

turbulences. Hence, large power aperture products are needed for the

detection of single pulse SNR, which needs large TX power and hence

increase in the cost.

However, detection is possible and the SNR can be brought up by

employing pulse compression, coherent integration32, FFT and spectral

averaging33 because the atmospheric returns are coherent within the beam

dwell times.

An active array of 576 TR modules providing a circular aperture of

120m diameter is realized at SDSC SHAR. The beams are tilted up to 20

degrees from zenith. It can provide height coverage of up to 21 km with a

resolution of 100m – 300m. It can provide one full wind profile every 15

minutes. It operates at 50 MHz frequency band so that it can provide data

up to mesospheric heights. It is a monostatic, coherent, pulsed Doppler

radar and the transmitted peak power is 576 kW. It operates with a PRF of

250 – 8000 Hz and pulse width is 0.5 to 32 µs. The digital receiver has

digital FIR filter with selectable impulse response and pass band. It provides

in-phase (I) and quadrature-phase (Q) outputs for further processing.

The subsystems of the Wind Profiler RADAR are

• Phased array antenna

• Feeder network

• Transmit Receive (TR) modules

• RF Exciter/Simulator

• 16 channel transceiver

• DBS receiver

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• Digital Receiver

• Digital Signal processing

• Beam Steering Unit,

• Timing Signal Generation, and

• Software

The data acquisition and processing scheme is shown in Figure 2.11.

Figure – 2.11 Data Acquisition and Processing scheme.

The digital signal processing system takes the I and Q data as input

and various processing modes are available and provides the output as a

Doppler spectrum. Various clutter filtering algorithms are also realized. The

processing modes include coherent integration (wavelet pre-processing34, No

coherent integration and Low Pass Filter), decoding, FFT, noise level

detection, spectral averaging, ground echo rejection, calculation of moments,

unfolding of Doppler velocity, checks for receiver power and spectrum width,

incoherent rejection and computation of U, V and W.

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Ground clutter filter and autonomously propagated (AP) clutter filters

are realized to provide >60 dB clutter cancellation. Data analysis for vertical

shear check and quadratic surface check are also provided. Various

techniques like Multi-Peak Picking (MPP), Signal Processing35,36 System

(SPS), National Centre for Atmospheric Research (NCAR) Improved Moments

Algorithm (NIMA) and Wind finding NCAR Winds and Confidence Algorithm

(NWCA) are used for signal identification.

In this chapter, the details of a C-Band Radar are provided for which

the detailed calibration is carried out using Satellite tracking. The

mathematical modeling, simulation and coefficients estimation in detail are

described in detail in Chapter-3 and Chapter-4. The calibrated Radar

measurements are used to estimate the state vector of PSLV, GSLV and

LVM3 launch vehicles using Linear Kalman Filter with model compensation

technique. The estimation process is described in detail in Chapter-5. In

Chapter-6, the LKF estimated state vector accuracy is well demonstrated in

generation of sustainer ignition command from ground for ATV vehicle.

Wind profiler Radar data processing and wind profile estimation methods

and results are provided in Chapter-7.